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Question
Find the area of the shaded region:
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Solution
∵ Diameter of complete circle = 14 cm
∴ Radius = `14/2` = 7 cm ...`[∵ "Radius" = "Diameter"/2]`
So, area of complete circle = πr2 = `22/7 xx 7 xx 7` = 154 cm2
∵ Diameter of small circle = `7/4`cm
∴ Radius = `7/(4 xx 2) = 7/8`cm
∴ Area of two small circles = 2 × πr2
= `2 xx 22/7 xx 7/8 xx 7/8`
= `77/16`cm2
∴ Area of shaded region = Area of complete circle – Area of two small circles
= `154 - 77/16`
= `(154 xx 16 - 77)/16` ...[Taking LCM]
= `(2464 - 77)/16`
= `2387/16`
= `149 3/16`cm2
Hence, the area of shaded region is `149 3/16`cm2.
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